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Air Changes per Hour Calculator

Find how many times an hour a fan or purifier changes a room's air (ACH), or the airflow (CFM) needed to reach a target.

Level: Grades 6–7

  • Common Core standard 6.RP.A.3.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
  • Common Core standard 6.G.A.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Printable worksheet

Air Changes per Hour Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for
Units

Cubic feet per minute delivered by the fan, purifier or supply vents.

Result

Air changes per hour

6.25 ACH

That airflow replaces the room's air about 6.25 times per hour.

Airflow in cubic meters per hour
169.9 m³/h
Minutes per air change
9.6 min
Room volume
960 ft³

See the step-by-step solution ↓

Step-by-step solution

  1. Find the room's volume (how much air it holds): length × width × height

    12×10×8=960 ft³

  2. Multiply the airflow by 60 to get air per hour, then divide by the room volume to count roomfuls

    100×60960=6.25 per hour

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how many times an hour a fan or purifier swaps out or cleans the air in your room. That number is called air changes per hour (ACH). It counts how often the room's air is replaced, or passed through a filter, in one hour. It's the airflow divided by the room's volume. So a fan that moves the room's whole volume of air every ten minutes gives six air changes per hour. People use the figure to compare ventilation fans, kitchen and bathroom exhaust fans, and portable air purifiers.

This calculator works both ways. Enter the room size and a fan's airflow to get the ACH it provides. Or enter a target ACH to find the airflow you need. Airflow is shown in cubic feet per minute (CFM) or cubic meters per hour. Recommended rates vary a great deal with the room and its use, so the target is yours to set.

Where it's used

Why this math matters outside the classroom:

  • Bathroom fans. A 50 CFM fan in an 8 × 5 × 8 ft bathroom (320 ft³) moves 3,000 ft³ an hour, about 9.4 air changes.
  • Workshop ventilation. Woodworkers size a fan by multiplying a 20 × 15 × 10 ft shop volume of 3,000 ft³ by a target ACH and dividing by 60.
  • Classroom air. Facilities staff check how often a 30 × 25 × 10 ft classroom's air is replaced from the CFM its ventilation system delivers.
  • Grow tents. Indoor gardeners size an exhaust fan so a 4 × 4 × 7 ft tent's 112 ft³ of air is swapped out about once a minute.
  • Minutes to hours. Students see why the formula multiplies by 60: fan airflow is rated per minute, but air changes are counted per hour.

Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3.d, 6.G.A.2. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what to solve for: air changes per hour, or the airflow needed.
  2. Pick US units (feet and CFM) or metric units (meters and m³/h).
  3. Enter the room's length, width and ceiling height. Then enter either the airflow or the target ACH.
  4. Read the result. You'll also see how long each air change takes and the airflow in other units.

What the inputs mean

Ceiling height
For sloped or vaulted ceilings, use the average height so the volume comes out right.
Airflow
Use the airflow the device really delivers. For purifiers, the figure to use is the clean air delivery rate (CADR). A fan's rating with nothing in its way overstates what it moves through ducts or filters.
Target air changes per hour
There's no single correct rate. Different codes and guidelines give very different targets to living spaces, workshops, kitchens and clean rooms. Use the figure that applies to your situation.

Formula and method

room volume = length × width × height
ACH = CFM × 60 ÷ room volume (ft³)
CFM needed = ACH × room volume (ft³) ÷ 60
metric: ACH = airflow (m³/h) ÷ room volume (m³)
1 CFM = 1.69901079552 m³/h;  minutes per air change = 60 ÷ ACH

In the formulas, ACH is air changes per hour and CFM is cubic feet of air per minute. Room volume is in cubic feet (ft³) or cubic meters (m³). CFM is a volume per minute, so multiplying by 60 gives the volume moved in an hour. Dividing that by the room's volume counts how many roomfuls of air pass through in the hour. Metric airflow is usually already given per hour, so there's no need for the 60.

Conversions use the exact cubic foot, 0.028316846592 m³. Liters per second is another common ventilation unit. It equals m³/h × 1,000 ÷ 3,600.

Worked example

A bedroom is 14 ft × 12 ft with an 8 ft ceiling, and an air purifier delivers 200 CFM.

  1. Room volume: 14 × 12 × 8 = 1,344 ft³.
  2. ACH: 200 × 60 ÷ 1,344 = 8.93 air changes per hour.
  3. Time per change: 60 ÷ 8.93 = 6.72 minutes.
  4. To aim for 5 ACH instead: 5 × 1,344 ÷ 60 = 112 CFM.

Result: The purifier cycles the bedroom's air about 8.93 times an hour; 112 CFM would be enough for 5 ACH.

Understanding the result

A higher ACH means the room's air is replaced or filtered more often. But each air change doesn't remove all of the original air. That's because incoming air mixes with what's already there. With perfect mixing, one air change replaces about 63% of the air, and three changes about 95%.

If you're comparing devices, compare them at the same room size. A unit that gives 4 ACH in a small room may give only 2 ACH in a room twice the volume.

Assumptions and limitations

  • The room is a rectangular box, or you've used its average ceiling height.
  • The airflow you enter is what the device really delivers, not a rating with nothing in its way.
  • Air in the room is well mixed.
  • Furniture and dead spots mean some parts of a room get less fresh air than the average figure suggests.
  • Fan airflow falls as filters clog up or ducts add resistance. So the real ACH can drop over time.
  • The calculator doesn't recommend a target rate. Requirements depend on local codes and how the room is used.

Frequently asked questions

How do I find the CFM needed for a room?

Multiply the room's volume in cubic feet by the target air changes per hour. Then divide by 60. A 1,000 ft³ room at 6 ACH needs 1,000 × 6 ÷ 60 = 100 CFM.

What is a good number of air changes per hour?

It depends on the room. Ordinary living spaces often get far less than one change per hour of outside air. Kitchens, bathrooms, workshops and healthcare spaces have their own, higher targets set by codes and standards. Check the guidance that applies to your building or use.

Does ACH count recirculated air?

The formula itself doesn't care where the air comes from. When the airflow is outdoor air, it measures ventilation (fresh air brought in). When it's a purifier's clean air delivery rate, it measures filtration (air cleaned and sent back). Be clear which one a target refers to.

How do I convert CFM to cubic meters per hour?

Multiply CFM by 1.699. For example, 100 CFM is about 169.9 m³/h, or about 47.2 liters per second.

How this calculator is checked

Method: Definition of air change rate: ACH = volumetric airflow per hour ÷ room volume. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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